There are many electronic appliances wherein an inductance element is installed, ferrite material is used for the electric signal line and the power line thereof, to prevent electromagnetic interference. FIG. 20(A) shows a model circuit of such electronic appliances. In FIG. 20(A), an inductance element 12 connects to the output end of inverter IC 10 whereto a voltage of 5 volts is placed, and line(cable) 14 connects to the output end of inductance element 12. Inverter IC 16 connects to the output end of line 14. FIG. 20(B) shows a frequency characteristic of the inductance element 12. In FIG. 20(B), Z, R, and X represent impedance, resistance part, and reactance part, respectively. As FIG. 20(B) shows, reactance component X decreases and resistance component R increases as the frequency becomes higher. When a pulse signal is input into such an electric signal line stated above, signals with wave forms as shown in FIG. 20(C) are read at the measurement point PD.
It is a common practice to depend on measured values in selecting an inductance element, and confirming what are the effects caused by the inserted element, and the like. However, if it is made possible to obtain results equivalent to measured values by simulations, measurement will no longer be necessary, and the time for reviewing may be shortened. Thus, to support this assumption, creating an equivalent circuit that demonstrates characteristics of the inductance element well is under study.
Generally, LsCpRp parallel equivalent circuit as shown in FIG. 21(A) is well known as the equivalent circuit stated above. This is a circuit wherein inductance Ls, capacitance Cp, and resistance Rp are in parallel connection. If circuit constants of an inductance element that has the same frequency characteristic as shown in FIG. 20(B) are determined by using such an equivalent circuit, the process is as follows.
First, impedance Z that represents the impedance of the whole equivalent circuit shown in FIG. 21(A) is given by the equation, Z=R+jX. In this equation, "R", "X", and "j" represents resistance component (real number), reactance component, and imaginary unit, respectively. Then, resistance component R and reactance component X are given by Expressions 1 and 2, respectively, as follows: ##EQU1## ##EQU2##
In these expressions, "f" represents frequency. In the frequency domain wherein resistance component R is small and the expression Z.apprxeq.jX holds, Expression 3 holds. When the frequency is 1 MHz, reactance component X measures 85 .OMEGA.. Substituting this value of X in Expression 3 yields Ls=13. 5 .mu.H. EQU X=27.pi.f.multidot.Ls Expression 3
Secondly, at the resonance point, Expression 4 holds.
Expression 4 EQU 1=(2.pi.f).sup.2 LsCp, R=Rp
With this Expression, Rp (measured value of resistance component R at the resonance point)=640 .OMEGA. is selected. Regarding Cp, substituting the values R=200 .OMEGA. (measured value of resistance component R at 1 G Hz), Ls=13.5 .mu.H, and Rp=640 .OMEGA. Expression 1 yields Cp=0.37 pF. Applying the selected values of circuit constants Ls=13.5 .mu.H, Rp=640 .OMEGA., and Cp=0.37 pF to the equivalent circuit of FIG. 21(A) gives the impedance characteristic as shown in FIG. 21(B).
Comparing FIG. 21(B) that shows a simulation result by making use of an equivalent circuit with FIG. 20(B) that shows measured values clearly indicates that there is a big difference between the two graphs, and that the equivalent circuit in FIG. 21(A) does not make an accurate analysis of the measured values. Especially, values of reactance component X at around 7.5 MHz are too large in FIG. 21(B). This indicates that structuring a simulator with the equivalent circuit in FIG. 21(A) does not bring about sufficiently accurate results.
Next, we are going to select circuit constants of an inductance element that has the same impedance frequency characteristic as shown in FIG. 22(A), by using the equivalent circuit of FIG. 21(A). Just as in the case of comparing FIG. 21(B) with FIG. 20(B), the value Ls=0.96 .mu.H is selected because a measured value of reactance component X at 10 MHz is 60 .OMEGA.. At the resonance point, the expressions 1=(2.pi.f).sup.2 LsCp and R=Rp hold. Therefore Rp (a measured value of resistance component R at the resonance point)=1170 .OMEGA. is selected. The value Cp=0.094 pF is found by substituting the values R=530 .OMEGA. (an actual value of "R" at 1.8 GHz), Ls=0.96 .mu.H, and Rp=1170 .OMEGA. in the said Expression 1.
Applying the selected values of circuit constants Ls=0.96 .mu.H, Rp=1170 .OMEGA., Cp=0.094 pF to the equivalent circuit of the FIG. 21(A) yields the impedance characteristic as shown in FIG. 22(B). There is a significant difference between FIG. 22(A) and FIG. 22(B). This indicates that the equivalent circuit of FIG. 21(A) does not make an accurate analysis of measured values. Especially, a value of reactance component X at around 200 MHz is too large in FIG. 22(B). In addition, in FIG. 22(B), the value of reactance component X is the largest at around 100 MHz, and values of resistance component R are smaller up to around 40 MHz. These are also differences from FIG. 22(A). This also indicates that the equivalent circuit in FIG. 21(A) does not make an accurate analysis of measured values.
These inconveniences is attributed to the fact that the frequency characteristic of the ferrite material used in inductance element 12 can not be demonstrated by the equivalent circuit of FIG. 21(A). It is well known that each ferrite material has its specific resonance frequency, and brings about phenomenon of magnetic resonance in the frequency domain above the level of the said specific resonance frequency. Therefore, permeability temporally decreases (when considering it as an inductance element, value decrease of reactance component X occurs), or increases at the specific oscillation frequency.